Properties

Label 14.89
Level $14$
Weight $0$
Character 14.1
Symmetry odd
\(R\) 13.23273
Fricke sign $+1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(13.2327363052090083356696244667 \pm 3 \cdot 10^{-8}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.27784612 \pm 9.2 \cdot 10^{-4} \)
\(a_{4}= +0.5 \) \(a_{5}= -1.95221923 \pm 7.1 \cdot 10^{-4} \) \(a_{6}= -0.90357365 \pm 9.2 \cdot 10^{-4} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.63289070 \pm 7.2 \cdot 10^{-4} \)
\(a_{10}= +1.38042745 \pm 7.1 \cdot 10^{-4} \) \(a_{11}= +1.69191848 \pm 7.3 \cdot 10^{-4} \) \(a_{12}= +0.63892306 \pm 9.2 \cdot 10^{-4} \)
\(a_{13}= +0.84174138 \pm 6.8 \cdot 10^{-4} \) \(a_{14}= +0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -2.49463576 \pm 8.8 \cdot 10^{-4} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.07676208 \pm 4.7 \cdot 10^{-4} \) \(a_{18}= -0.44752131 \pm 7.2 \cdot 10^{-4} \)
\(a_{19}= +0.58267929 \pm 7.0 \cdot 10^{-4} \) \(a_{20}= -0.97610961 \pm 7.1 \cdot 10^{-4} \) \(a_{21}= -0.48298043 \pm 9.2 \cdot 10^{-4} \)
\(a_{22}= -1.19636703 \pm 7.3 \cdot 10^{-4} \) \(a_{23}= -0.35641533 \pm 6.4 \cdot 10^{-4} \) \(a_{24}= -0.45178683 \pm 9.2 \cdot 10^{-4} \)
\(a_{25}= +2.81115991 \pm 5.5 \cdot 10^{-4} \) \(a_{26}= -0.59520104 \pm 6.8 \cdot 10^{-4} \) \(a_{27}= -0.46910919 \pm 6.8 \cdot 10^{-4} \)
\(a_{28}= -0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -0.71089271 \pm 7.9 \cdot 10^{-4} \) \(a_{30}= +1.76397386 \pm 1.6 \cdot 10^{-3} \)
\(a_{31}= -0.89697814 \pm 7.8 \cdot 10^{-4} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +2.16201146 \pm 8.7 \cdot 10^{-4} \)
\(a_{34}= +0.05427899 \pm 4.7 \cdot 10^{-4} \) \(a_{35}= +0.73786951 \pm 7.1 \cdot 10^{-4} \) \(a_{36}= +0.31644535 \pm 7.2 \cdot 10^{-4} \)
\(a_{37}= -0.34811146 \pm 5.6 \cdot 10^{-4} \) \(a_{38}= -0.41201648 \pm 7.1 \cdot 10^{-4} \) \(a_{39}= +1.07561595 \pm 7.9 \cdot 10^{-4} \)
\(a_{40}= +0.69021373 \pm 7.1 \cdot 10^{-4} \) \(a_{41}= -0.90762215 \pm 4.6 \cdot 10^{-4} \) \(a_{42}= +0.34151874 \pm 9.2 \cdot 10^{-4} \)
\(a_{43}= -0.78019955 \pm 7.2 \cdot 10^{-4} \) \(a_{44}= +0.84595924 \pm 7.3 \cdot 10^{-4} \) \(a_{45}= -1.23554139 \pm 6.3 \cdot 10^{-4} \)
\(a_{46}= +0.25202370 \pm 6.4 \cdot 10^{-4} \) \(a_{47}= -1.18365848 \pm 5.1 \cdot 10^{-4} \) \(a_{48}= +0.31946153 \pm 9.2 \cdot 10^{-4} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -1.98779024 \pm 5.5 \cdot 10^{-4} \) \(a_{51}= -0.09809013 \pm 5.6 \cdot 10^{-4} \)
\(a_{52}= +0.42087069 \pm 6.8 \cdot 10^{-4} \) \(a_{53}= -0.35634077 \pm 6.9 \cdot 10^{-4} \) \(a_{54}= +0.33171029 \pm 6.8 \cdot 10^{-4} \)
\(a_{55}= -3.30299579 \pm 6.7 \cdot 10^{-4} \) \(a_{56}= +0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= +0.74457447 \pm 1.0 \cdot 10^{-3} \)
\(a_{58}= +0.50267705 \pm 7.9 \cdot 10^{-4} \) \(a_{59}= +0.90663004 \pm 7.4 \cdot 10^{-4} \) \(a_{60}= -1.24731788 \pm 1.6 \cdot 10^{-3} \)

Displaying $a_n$ with $n$ up to: 60 180 1000